I think this corrosion comes from sweat. How can this be removed?
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I don't think you can. It looks to me like the anodized surface layer has worn off, exposing the plain aluminum.
I have exactly the same 'stains' on my 2003 Centaur Ergopower levers, which I also attributed to the layer of anodization wearing off. It is not corrosion.
Different thermal expansion rates of the oxide and the alloy underneath could damage the layer of anodization. Not sure if the presence of mildy acidic human sweat could accelerate the process significantly.
You cannot 'clean' the lever, although technically you could get it anodized again (or buy new carbon levers which do not have THIS problem -- they have a protective veneer which chips away..).